# How to Calculate the Capital Asset Pricing Model (CAPM)

The capital asset pricing model is often called CAPM for short. It is an investment theory that shows the relationship between the expected return of an investment and market risk. So CAPM is a formula that's used to calculate the expected return of security given its level of systemic risk. So in our formula, we got the expected return of security on the left side which is Ri. That expected return (Ri) is equal to the risk-free rate of return, that's a rate of return you would earn on an investment that has zero risk for example you might say a three-month US Treasury bill. Let's say the rate of return on that was 1.25% then that would be your risk-free rate and then you add to that the beta (βi) of security. So the beta is a measure of the systemic risk of this security.

So we've got this measure of systemic risk beta and then we multiply that by this whole market risk premium. The market risk premium is the expected return of the market minus the risk-free rate. So when we take the market risk premium, we multiply it by the beta of that security and then we add the risk-free rate that's going to tell us the expected return of security (Ri). So this whole thing is the Capital Asset Pricing Model or CAPM.

By the way, so you'll sometimes hear it was somebody talking about a stock if someone thought about the stock in Microsoft or Caterpillar or some company you might hear them talking about the cost of equity capital and that is the same as this thing s Ri in our formula. So this expected return of security Ri this return is basically the return that investors expect to receive given the level of risk that they are bearing, how much risk are they're bearing? Well, that's what bata tells us. So when we say what is the cost of equity capital for caterpillar shareholders and we're thinking about stock in Caterpillar let's say it was 9.21%. That's what it's telling us is that's the expected return of Caterpillar stock that someone would be expecting. So we'd say that's the cost of equity capital.

Now I'm gonna write some more articles on CAPM but one thing I really want you to know is that what is the implication here of the capital asset pricing model. That is the more systemic risk that the security has, it's going to be the higher return that the investors are expecting. So here's our measure of systemic risk which is that beta if beta let's say that was 1.25 and then we were to increase it to 3. So the higher we make this beta the higher is going to be the expected return of the security. If you are an investor and I tell you to look it's actually this investment is riskier, it's instead of the risk being 1.25 it's 3 or it's 4 or something like that, the more risky the security is which is measured here by beta, the higher the return you are going to want to receive because you are wanting as an investor to be compensated for barring that risk.

Herewith the capital asset pricing model, we're assuming just that there's a single factor, we'll later go in and add additional factors. So there's actually more and what we'll talk about multi-factor models in the future but for right now this is a single factor model. We're really just looking at this market risk premium times the amount of systemic risk and then we add that to the risk-free rate and that is telling us the return that the investors in that security expect to receive given these factors.